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Deep Neural Collapse (DNC) refers to the surprisingly rigid structure of the data representations in the final layers of Deep Neural Networks (DNNs).
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Max A Woodbury · 1950
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Kernel methods for deep learning
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Libin Zhu, Chaoyue Liu, Adityanarayanan Radhakrishnan, and Mikhail Belkin · 2009
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The spectrum of kernel random matrices
Noureddine El Karoui · 2010
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A consistent estimator of the expected gradient outerproduct
Shubhendu Trivedi, Jialei Wang, Samory Kpotufe, and Gregory Shakhnarovich · 2014
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Convex learning of multiple tasks and their structure
Carlo Ciliberto, Youssef Mroueh, Tomaso Poggio, and Lorenzo Rosasco · 2015
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A random matrix perspective on mixtures of nonlinearities for deep learning
Ben Adlam, Jake Levinson, and Jeffrey Pennington · 2019
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The neural tangent kernel in high dimensions: Triple descent and a multi-scale theory of generalization
Ben Adlam and Jeffrey Pennington · 2020
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Zhiyuan Li, Yuping Luo, and Kaifeng Lyu · 2020
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Neural collapse with unconstrained features
Dustin G Mixon, Hans Parshall, and Jianzong Pi · 2020
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Prevalence of neural collapse during the terminal phase of deep learning training
Vardan Papyan, X. Y. Han, and David L Donoho · 2020
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Explicit regularization and implicit bias in deep network classifiers trained with the square loss
Tomaso Poggio and Qianli Liao · 2020
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Exploring deep neural networks via layer-peeled model: Minority collapse in imbalanced training
Cong Fang, Hangfeng He, Qi Long, and Weijie J Su · 2021
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Improved generalization bounds for transfer learning via neural collapse
Tomer Galanti, András György, and Marcus Hutter · 2022
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Linking neural collapse and l2 normalization with improved out-of-distribution detection in deep neural networks
Jarrod Haas, William Yolland, and Bernhard T Rabus · 2022
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Neural collapse under mse loss: Proximity to and dynamics on the central path
X. Y. Han, Vardan Papyan, and David L Donoho · 2022
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A law of data separation in deep learning
Hangfeng He and Weijie J Su · 2022
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Universality laws for high-dimensional learning with random features
Hong Hu and Yue M Lu · 2022
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Mechanism of feature learning in convolutional neural networks
Daniel Beaglehole, Adityanarayanan Radhakrishnan, Parthe Pandit, and Mikhail Belkin · 2023
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Kernel learning in ridge regression" automatically" yields exact low rank solution
Yunlu Chen, Yang Li, Keli Liu, and Feng Ruan · 2023
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Neural collapse for unconstrained feature model under cross-entropy loss with imbalanced data
Wanli Hong and Shuyang Ling · 2023
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Neural collapse: A review on modelling principles and generalization
Vignesh Kothapalli · 2023
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Neural collapse in the intermediate hidden layers of classification neural networks
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Wenlong Ji, Yiping Lu, Yiliang Zhang, Zhun Deng, and Weijie J Su · 2022
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The asymmetric maximum margin bias of quasi-homogeneous neural networks
Daniel Kunin, Atsushi Yamamura, Chao Ma, and Surya Ganguli · 2022
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Neural collapse under cross-entropy loss
Jianfeng Lu and Stefan Steinerberger · 2022
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Imbalance trouble: Revisiting neural-collapse geometry
Christos Thrampoulidis, Ganesh Ramachandra Kini, Vala Vakilian, and Tina Behnia · 2022
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Extended unconstrained features model for exploring deep neural collapse
Tom Tirer and Joan Bruna · 2022
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Perturbation analysis of neural collapse
Tom Tirer, Haoxiang Huang, and Jonathan Niles-Weed · 2022
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Linear convergence analysis of neural collapse with unconstrained features
Peng Wang, Huikang Liu, Can Yaras, Laura Balzano, and Qing Qu · 2022
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Liam Parker, Emre Onal, Anton Stengel, and Jake Intrater · 2023
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Feature learning in deep classifiers through intermediate neural collapse
Akshay Rangamani, Marius Lindegaard, Tomer Galanti, and Tomaso Poggio · 2023
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On the robustness of neural collapse and the neural collapse of robustness
Jingtong Su, Ya Shi Zhang, Nikolaos Tsilivis, and Julia Kempe · 2023
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Deep neural collapse is provably optimal for the deep unconstrained features model
Peter Súkeník, Marco Mondelli, and Christoph Lampert · 2023
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Perturbation analysis of neural collapse
Tom Tirer, Haoxiang Huang, and Jonathan Niles-Weed · 2023
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How far pre-trained models are from neural collapse on the target dataset informs their transferability
Zijian Wang, Yadan Luo, Liang Zheng, Zi Huang, and Mahsa Baktashmotlagh · 2023
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Dynamics in deep classifiers trained with the square loss: Normalization, low rank, neural collapse, and generalization bounds
Mengjia Xu, Akshay Rangamani, Qianli Liao, Tomer Galanti, and Tomaso Poggio · 2023
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Efficient estimation of the central mean subspace via smoothed gradient outer products
Gan Yuan, Mingyue Xu, Samory Kpotufe, and Daniel Hsu · 2023
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Daniel Beaglehole, Ioannis Mitliagkas, and Atish Agarwala · 2024
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Neural collapse versus low-rank bias: Is deep neural collapse really optimal?
Peter Súkeník, Marco Mondelli, and Christoph Lampert · 2024
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